473 to the Power of 3 = 473 3 = 105823817
473 to the power of 3 = 105823817
Welcome to our exponent calculator! We're exploring the concept of "473 to the power of 3". Let's break down what this means and how to calculate it.
What are Exponents?
An exponent is a mathematical operation where we multiply a number (called the base) by itself a certain number of times (indicated by the power or exponent). In our case, 473 is the base, and 3 is the exponent.
Calculation
To calculate 473 to the power of 3, we multiply 473 by itself 3 times. Here's the step-by-step process:
| Step | Calculation | Result |
|---|---|---|
| 1 | 473 | 473 |
| 2 | 473 × 473 | 223729 |
| 3 | 473 × 473 × 473 | 105823817 |
Solution: 473 to the power of 3 is equal to 105823817.
How to write 473 to the power of 3 ?
Step 1: Understand the Concept
"473 to the power of 3" means we're multiplying 473 by itself 3 times. Let's break this down:
Step 2: Learn the Notation
In mathematics, we have a special way to write this more concisely. We use superscript notation:
Here, 473 is called the "base", and 3 is called the "exponent" or "power".
Step 3: Understand Alternative Notations
Sometimes, especially when typing or in programming, you might see it written as:
This means the same thing as 4733.
Step 4: Calculate the Result
If we actually compute this:
Practice
Try writing these on your own:
- 472 to the power of 2
- 474 to the power of 4
- 3 to the power of 473
Interactive Power Calculator
Similar Calculations:
| Number | Power | Answer |
|---|---|---|
| 474 | 3 | 4743 = 106496424 |
| 475 | 3 | 4753 = 107171875 |
| 476 | 3 | 4763 = 107850176 |
Related Mathematical Operations
Square Root
The square root is the inverse operation of squaring a number. For our example:
v107850176 ≈ 10,385.0939
This is approximate because 473^3 isn't a perfect square.
Logarithm
Logarithms are the inverse of exponential functions. The logarithm of 107850176 with base 473 should equal 3:
log473(107850176) = 3
Exponent Properties
1. Multiplying exponents with the same base: 473a * 473b = 473(a+b)
Example: 4732 * 4733 = 4735 = 23675856753593
2. Dividing exponents with the same base: 473a / 473b = 473(a-b)
Example: 4735 / 4732 = 4733 = 105823817